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In database structures, two quantities are generally of interest: the average number of comparisons required to 1. Find an existing random record, and 2. Insert a new random ...

F_k[P_N(k)](x)=F_k[exp(-N|k|^beta)](x), where F is the Fourier transform of the probability P_N(k) for N-step addition of random variables. Lévy showed that beta in (0,2) for ...

The adjective "affine" indicates everything that is related to the geometry of affine spaces. A coordinate system for the n-dimensional affine space R^n is determined by any ...

Consider the distribution of distances l between a point picked at random in the interior of a unit cube and on a face of the cube. The probability function, illustrated ...

To generate random points over the unit disk, it is incorrect to use two uniformly distributed variables r in [0,1] and theta in [0,2pi) and then take x = rcostheta (1) y = ...

Sphere tetrahedron picking is the selection of quadruples of of points corresponding to vertices of a tetrahedron with vertices on the surface of a sphere. n random ...

Consider the average length of a line segment determined by two points picked at random in the interior of an arbitrary triangle Delta(a,b,c) with side lengths a, b, and c. ...

Ball point picking is the selection of points randomly placed inside a ball. n random points can be picked in a unit ball in the Wolfram Language using the function ...

Given a unit circle, pick two points at random on its circumference, forming a chord. Without loss of generality, the first point can be taken as (1,0), and the second by ...

Given a triangle with one vertex at the origin and the others at positions v_1 and v_2, one might think that a random point inside the triangle would be given by ...